The [Y] parameters of the network shown below are given as :
\(\begin{bmatrix}\dfrac{1}{R_1} & 0\\[4pt] 0 & 0\end{bmatrix}\)
What the Y parameters mean. They are the short-circuit admittance parameters, defined by
\(I_1=Y_{11}V_1+Y_{12}V_2, \qquad I_2=Y_{21}V_1+Y_{22}V_2\)
Each one is measured with the other port shorted, which is what makes them quick to read off a picture.
Read the topology. R1 hangs directly across port 1. The bottom rail is common to both ports, but the top terminal of port 2 is isolated — nothing joins it to the R1 node. So no current can ever enter or leave the upper terminal of port 2.
Step 1 — the two parameters with V2 shorted. Set V2 = 0 and apply V1. The whole of V1 sits across R1:
\(Y_{11}=\left.\dfrac{I_1}{V_1}\right|_{V_2=0}=\dfrac{1}{R_1}\)
Because port 2's upper terminal is open, that current cannot reach it:
\(Y_{21}=\left.\dfrac{I_2}{V_1}\right|_{V_2=0}=0\)
Step 2 — the two parameters with V1 shorted. Now drive port 2. Since its top terminal connects to nothing, no current flows anywhere:
\(Y_{22}=\left.\dfrac{I_2}{V_2}\right|_{V_1=0}=0, \qquad Y_{12}=\left.\dfrac{I_1}{V_2}\right|_{V_1=0}=0\)
Step 3 — assemble the matrix.
\([Y]=\begin{bmatrix}1/R_1 & 0\\ 0 & 0\end{bmatrix}\)
Where the distractors come from. Option 1 is the answer you would get if R1 were a shunt element common to both ports, i.e. if the two upper terminals were joined — then every entry becomes 1/R1 and the matrix is singular. Option 4 is the Y matrix of two independent resistors, one across each port. Option 2 is not even symmetric, so it cannot describe a reciprocal network built only from resistors — a useful one-second check, since reciprocity demands Y12 = Y21.
A note on existence. This network has a perfectly good Y matrix even though its Z matrix does not exist — with port 2 open the impedance parameters run to infinity. That asymmetry is the practical reason both descriptions are kept in circuit theory.
Hence, \([Y]=\begin{bmatrix}1/R_1 & 0\\ 0 & 0\end{bmatrix}\).
Similar Questions
Assertion (A) : In a two port network, with 4 terminals four types of parameters like impedance, admittance, hybrid and transmission are considered and they are related to each other.
Reason (R) : The assumption made for the above statement is that there are no independent sources and non-zero initial conditions within the linear port network.
Select your answer using the codes given below :
Read the following statements :
ST 1 : y-parameters can be obtained from Z parameters.
ST 2 : It is not necessary to define y-parameters separately.Match the given lists :
List – I List – II a. Condition of reciprocity i. \(\dfrac{Z_{12}}{Z_{22}}\) b. h12 ii. Z12 = Z21 c. 
\(\begin{bmatrix}R&R\\R&R\end{bmatrix}\)iii. Z d. Condition of symmetry iv. Z11 = Z22 Codes :
Important Questions from Two Port Networks
A Two - port network is reciprocal if and only if:
Read the following statements regarding two port networks.
(A) The condition of reciprocity and symmetry for a two-port network with 'g' parameter representation can be deduced from the interrelationship of 'h' and g parameters.
(B) The condition of reciprocity for the h parameter representation leads to the condition of reciprocity for 'g' parameters representation as g 12 = −g 21 .
(C) The condition of symmetry in h-parameters representation never leads to the condition of symmetry in 'g' parameters representation.
(D) The symmetry condition in 'h' and 'g parameter representation can be deduced by putting h 11 = g 11 .
Choose the correct answer from the options given below:
A passive 2-port network is in a steady-state. Compared to its input, the steady state output can never offer ________.
The condition for symmetric property of ABCD parameter of two port network is:
- When port 1 of two-port circuit is short-circuited, I 1 = 4I 2 & V 2 = 0.25 I 2 . Which of the following is true?
